Analytification conjecture for the closed string mirror

Let $\mathcal{R}$ be an eigenray diagram, let $Y_\mathcal{R}$ be the non-proper scheme over the Novikov field obtained from the associated toric variety by the stated Kaliman modifications, and let $\mathcal{Y}_\mathcal{R}$ be the rigid analytic mirror appearing in the paper. Analytification conjecture. $\mathcal{Y}_\mathcal{R}$ is the analytification of $Y_\mathcal{R}$. The authors strongly believe this gives a concrete global description of the mirror, but the statement is presented as an expectation and remains unproved.